I believe there isn't any, it's just clever use of the post mechanics.

You could do the following: use the quote option on the post with the animations, then watch how they are done.

For example, if you see a spoiler tab in the quote, the text is between the {spoiler} and the {/spoiler} (with cases insted btw).

Use the quote button to see my example:

Borage is too cute for any player in Fantasica.

Study the various commands that appear in the quote, and you'll see how they can be added.

I hope my explanation helped. If not, you could ask any of the moderators or forum designers for a quick Q&A.

Edit: Once you know how to work with the images, you can find the unit animations here: http://www.fantasicawiki.com/wiki/Main_Page - search for a unit, then copy the URL from the animation inside the box in the top right section of the page.